Question

Ethanol (C2H5OH) melts at -114 °C. The enthalpy of fusion is 5.02 kJ/mol. The specific heats of solid and liquid ethanol are 0.97 J/g-K and 2.3 J/g-K, respectively. How much heat (kJ) is needed to convert 25.0 g of solid ethanol at -135 °C to liquid ethanol at -60 °C?

A. 207.3
B. -13.3
C. 6.34
D. 3617
E. 8.63

Answer 1

Before you get started, lets change 5.02 kJ/mol to J/g to make everything more consistent.

1 mole of ethanol = 46g, so 5.02 kJ / mol = 5.02 kJ/ 46 g = 0.109 kJ/g or 109 J/g

Now consider the warming of ethanol in three steps.

1 Solid warming from -135 to -114. Delta t = 21 C

q = m c delta t
q = 25 g x 0.97 J/g C x 21 C = 509 J    -----------      q1

2. Solid at -114 turning to liquid at -114

q = m Kf
q = 25 g x 109 J / g = 2725 J   ------------------ q2

3. Liquid warming from -114 to -60 C Delta t = 54 C

q = m c delta t
q = 25 g x 2.3 J/g/C x 54 = 3150 J    ------------------- q3
--------------------------------------...
Total energy q = q1 + q2 + q3 = 509 J + 2725 J + 3150 J = 6339J or 6.34 kJ

option c is correct